An efficient initial guess formation of broken-symmetry solutions by using localized natural orbitals

Subsystem density-functional theory: A reliable tool for spin-density based properties

Subsystem density-functional theory compiles a set of features that allow for efficiently calculating properties of very large open-shell radical systems such as organic radical crystals, proteins, or deoxyribonucleic acid stacks. It is computationally less costly than correlated ab initio wave function approaches and can pragmatically avoid the overdelocalization problem of Kohn-Sham density-functional theory without employing hard constraints on the electron-density. Additionally, subsystem density-functional theory calculations commonly start from isolated fragment electron densities, pragmatically preserving a priori specified subsystem spin-patterns throughout the calculation. Methods based on subsystem density-functional theory have seen a rapid development over the past years and have become important tools for describing open-shell properties. In this Perspective, we address open questions and possible developments toward challenging future applications in connection with subsystem density-functional theory for spin-dependent properties.

Weak O2 binding and strong H2O2 binding at the non-heme diiron center of trypanosome alternative oxidase

Alternative oxidase (AOX) catalyzes the four-electron reduction of dioxygen to water as an additional terminal oxidase, and the catalytic reaction is critical for the parasite to survive in its bloodstream form. Recently, the X-ray crystal structure of trypanosome alternative oxidase (TAO) complexed with ferulenol was reported and the molecular structure of the non-heme diiron center was determined. The binding of O₂ was a unique side-on type compared to other iron proteins. In order to characterize the O₂ binding state of TAO, the O₂ binding states were searched at a quantum mechanics/molecular mechanics (QM/MM) theoretical level in the present study. We found that the most stable O₂ binding state is the end-on type, and the binding states of the side-on type are higher in energy. Based on the binding energies and electronic structure analyses, O₂ binds very weakly to the TAO iron center (ΔE =6.7 kcal mol^-1) in the electronic state of Fe(II)…OO, not in the suggested charge transferred state such as the superoxide state (Fe(III)OO· ^-) as seen in hemerythrin. Coordination of other ligands such as water, Cl^-, CN^-, CO, N₃^- and H₂O₂ was also examined, and H₂O₂ was found to bind most strongly to the Fe(II) site by ΔE = 14.0 kcal mol^-1. This was confirmed experimentally through the measurement of ubiquinol oxidase activity of TAO and Cryptosporidium parvum AOX which was found to be inhibited by H₂O₂ in a dose-dependent and reversible manner.

Subsystem density-functional theory for interacting open-shell systems: spin densities and magnetic exchange couplings

We investigate the possibility of describing interacting open-shell systems in high-spin and broken-symmetry (BS) states with subsystem density-functional theory (sDFT). This subsystem method typically starts from the electronic-structure results obtained for individual systems, for which the spin states can be individually defined. Through the confining effect of the embedding potential and/or the use of monomer basis sets, these individual spin states can be preserved in sDFT calculations. This offers the possibility of easy convergence to broken-symmetry states with arbitrary local spin patterns. We show that the resulting spin densities are in very good agreement with successfully converged broken-symmetry Kohn-Sham density-functional theory (KS-DFT) calculations. Yet sDFT can even cure those BS cases where KS-DFT suffers from convergence problems or convergence to undesired spin states. In contrast to KS-DFT, the sDFT-results only show a mild exchange-correlation functional dependence. We also show that magnetic coupling constants from sDFT are not satisfactory with standard approximations for the non-additive kinetic energy. When this component is evaluated "exactly", i.e. based on potential reconstruction, however, the magnetic coupling constants derived from spin-state energy differences are greatly improved. Hence, the interacting radicals studied here represent cases where even (semi-)local approximations for the non-additive kinetic-energy potential work well, while the parent energy functionals do not yield satisfactory results for spin-state energy differences.

Characterization of charge transfer excited states in [2Fe–2S] iron–sulfur clusters using conventional configuration interaction techniques

The experimental UV–Vis spectra of the biologically relevant [2Fe–2S] iron–sulfur clusters feature typically three bands in the 300–800 nm range. Based on ground-state orbitals and using the one electron transition picture, these bands are said to be of charge transfer character. The key complication in the electronic structure calculations of these compounds are the antiferromagnetic coupling of the iron centers and high covalency of Fe–S bonds. Thus, the examples of the direct computations of electronically excited states of these systems are rare. Whereas low lying electronic excited states were subject of recent studies, higher energy states computed with many-body theories were never reported. In this work we present, for the first time, calculations of the electronic spectra of [Fe2S2](SMe)42− biomimetic compound. We demonstrate that spin-averaged restricted open-shell Hartree–Fock orbitals are superior to high-spin orbitals and are convenient reference for subsequent configuration interaction calculations. Moreover, the use of conventional configuration interaction methods enabled us to study the nature of the excited states in details with the difference density maps. By systematic extension of the donor orbital space we show that key excitations in the 300–800 nm range are of Fe 3d ← (μ-S) character.

Structural Changes of the Trinuclear Copper Center in Bilirubin Oxidase upon Reduction

Geometric and electronic structure changes in the copper (Cu) centers in bilirubin oxidase (BOD) upon a four-electron reduction were investigated by quantum mechanics/molecular mechanics (QM/MM) calculations. For the QM region, the unrestricted density functional theory (UDFT) method was adopted for the open-shell system. We found new candidates of the native intermediate (NI, intermediate II) and the resting oxidized (RO) states, i.e., NI^H+ and RO₀. Elongations of the Cu-Cu atomic distances for the trinuclear Cu center (TNC) and very small structural changes around the type I Cu (T1Cu) were calculated as the results of a four-electron reduction. The QM/MM optimized structures are in good agreement with recent high-resolution X-ray structures. As the structural change in the TNC upon reduction was revealed to be the change in the size of the triangle spanned by the three Cu atoms of TNC, we introduced a new index (l) to characterize the specific structural change. Not only the wild-type, but also the M467Q, which mutates the amino acid residue coordinating T1Cu, were precisely analyzed in terms of their molecular orbital levels, and the optimized redox potential of T1Cu was theoretically reconfirmed.

Redox Potential-Dependent Formation of an Unusual His-Trp Bond in Bilirubin Oxidase

Bilirubin oxidase (BOD) belongs to the family of blue multicopper oxidases, and catalyzes the concomitant oxidation of bilirubin to biliverdin and the reduction of molecular oxygen to water via a four-electron reduction system. The active sites of BOD comprise four copper atoms; type I copper (T1Cu) forms a mononuclear site, and a cluster of three copper atoms forms a trinuclear center. In the present study, we determined the high-resolution crystal structures of BOD from the fungus Myrothecium verrucaria. We investigated wild-type (WT) BOD and a BOD mutant called Met467Gln, which is inactive against bilirubin. The structures revealed that a novel post-translational crosslink between Trp396 and His398 is formed in the vicinity of the T1Cu site in WT BOD, whereas it is absent in the Met467Gln mutant. Our structural and computational studies suggest that the His-Trp crosslink adjusts the redox potential of T1Cu to that of bilirubin to efficiently abstract electrons from the substrate.

Geometric and electronic structures of the synthetic Mn₄CaO₄ model compound mimicking the photosynthetic oxygen-evolving complex

Water oxidation by photosystem II (PSII) converts light energy into chemical energy with the concomitant production of molecular oxygen, both of which are indispensable for sustaining life on Earth. This reaction is catalyzed by an oxygen-evolving complex (OEC) embedded in the huge PSII complex, and its mechanism remains elusive in spite of the extensive studies of the geometric and electronic structures. In order to elucidate the water-splitting mechanism, synthetic approaches have been extensively employed to mimic the native OEC. Very recently, a synthetic complex [Mn4CaO4(Bu(t)COO)8(py)(Bu(t)COOH)2] (1) closely mimicking the structure of the native OEC was obtained. In this study, we extensively examined the geometric, electronic and spin structures of 1 using the density functional theory method. Our results showed that the geometric structure of 1 can be accurately reproduced by theoretical calculations, and revealed many similarities in the ground valence and spin states between 1 and the native OEC. We also revealed two different valence states in the one-electron oxidized state of 1 (corresponding to the S2 state), which lie in the lower and higher ground spin states (S = 1/2 and S = 5/2), respectively. One remarkable difference between 1 and the native OEC is the presence of a non-negligible antiferromagnetic interaction between the Mn1 and Mn4 sites, which slightly influenced their ground spin structures (spin alignments). The major reason causing the difference can be attributed to the short Mn1-O5 and Mn1-Mn4 distances in 1. The introduction of the missing O4 atom and the reorientation of the Ca coordinating ligands improved the Mn1-O5 and Mn1-Mn4 distances comparable to the native OEC. These modifications will therefore be important for the synthesis of further advanced model complexes more closely mimicking the native OEC beyond 1.